Proposed Canon

Golems are magically animated Units. Frequently they are humanoid, but this is not a requirement. If a golem is destroyed, the remains can still be salvaged by a caster of the appropriate discipline.

When a caster creates a golem, they effectively imprint a tiny fragment of their own g-string onto the Stuff of the golem, giving it a minuscule string of its own. As a caster becomes more skilled at creating golems, they increase the size and complexity of this string fragment, allowing them to create more capable golems. Normal golems cannot modify their own strings, meaning they are unable to learn. The theory needed to accomplish this task is considered OP by the Thinkamancers.Erf-b3-p274

Thinkamancers also know a secret spell to take control of an enemy golem, but it requires a turn's worth of juice for "a few seconds of action at best."Erf-b3-p178

Dollamantic Golems

An LFN and G-RAF cloth golem, along with two Battle Bears and other RCC units.

Dollamancy golems come in a variety of forms, including Cloth Golems and Action Figures. They are built by, repaired by and receive combat bonuses from Dollamancers. Some Dollamancy units, such as Cloth Golems, can be further subdivided into individual types. Cloth Golems have the appearance of oversized stuffed animals, while Tchotchkes have the appearance of glass animals. Some, but not all, Dollamancy golems are heavy units.

Different Dollamancers appear to have preferences for a specific type of golem. Holly Shortcake was well known as a Dollamancer who created many cloth golems. Ace Hardware, on the other hand, prefers Action Figures.

According to Ace Hardware, Battle Bears and LFNs take multiple turns to assemble and it is likely that this limitation applies to other cloth golems as well.

Etsies are extremely simple cloth golems created by Archons. They cannot perform any useful functions, but are automatically killed by unled stacks, and thus serve as a warning system.

Dirtamantic Golems

Dirtamantic Golems are created by Dirtamancers out of various earthen materials - stones, rocks, metal, and, erm, "soil," or Crap. They can be healed by and receive bonuses from Dirtamancers. Known types include Crap, Metal, and Rock (Soft, Hard, and Acid).

Hat Magic Golems

Known Users

Types

Snow golems - The only known example was made of only three large balls of snow, with sticks for arms and small black rocks for features.

Speculation

Other Possible Golem Types

There are several units that have not been explicitly been called "golems," but share many of the same characteristics of golems. Scarecrows, Molls, and Dolls are all non-living units that are animated by magic.TBFGK Epilogue 13 However, it is not clear whether they are truly golems, which are created and designed by their caster, or if they fall more properly in the broader category of non-living units that use existing material (like uncroaked units which, while non-living and animated, use the corpses of the croaked as their medium).

It may be possible to create as yet unseen types of Golems from material such as wood or flesh.

Golems as Turing machines

Golems (or possibly all units) may act like Turing machines, with the G-string playing the role of the infinitely long tape. There are some subtle hints in this direction in the comic.

Golems are animated by being given a small piece of the caster's string. This is enough for them to perform simple actions. The more advanced the caster, the larger the string fragment they can give, which allows the golem to perform more complex actions. This is consistent with the Turing machine model, with a larger instruction set (read from the tape/string) giving rise to a more complex program.

We're also told that learning means being able to write to one's own string. In the Turing model, this may correspond to self-modifying code, or simply being able to store information in memory. Golems don't have the ability to write to their own strings/tapes, so they cannot learn. They can only run the program they were given.

Ordinary units, or at least Isaac, have a "fantastically long string" compared to a golem's "tiny" one.Erf-b3-p287 When Claud joins up with Big Think, he thinks the string comprising the State 8.2 link might be infinite. Erf-b3-p274 He also begins to work the string in a mechanical way which is exactly like a Turing machine:

The knowledge was practically the only thing he knew, so he proceeded to put it to use, one thread-pair at a time. Those are right, go forward. That's wrong, go forward another. Also wrong, forward a third time. Looks right. So go back two, confirm it's wrong, switch the threads, forward one, switch, then back two, check-check-check and see right-right-right, okay. Go forward. This one's wrong...Erf-b3-p274

To run, in this context, may mean to execute, as in a computer program.

Real World References

The names of the different types of Rock Golems (including Metal Golems) are references to genres of Rock 'n Roll music. Furthermore, the physical shape of each type of golem is reminiscent of the type of music they represent. For instance, in the case of the Soft Rock Golem shown above, the image looks strikingly similar to soft rocker Paul Simon circa 1968.[1] Similarly, four (presumed) Hard Rock Golems shown croaking a stack of marbit bear a striking resemblance to theme-rock band KISS.Erf-b1-p087[2] One of the other golems (possibly metal?) was stylized after the Comedian from the graphic novel The Watchmen.

Of the depicted Crap Golems, one is clearly identifiable as a dinosaur, one is a dalek from the television show Doctor Who and another resembles the titular character of the Schlock Mercenary webcomic.[3]